I run Arch on my RPi, which means installing things is super easy. Someone wrote up some software to do this streaming called mjpg-streamer.
$ sudo pacman -S mjpg-streamer
Once this installs the software is relatively simple to run. The options are defined as follows:
-d - USB Webcam (or video device)
-r - Resolution
-f - Frame Rate
-p - Port Number
-w -Web directory
An example of running the software:
$ mjpg_streamer -i "/usr/lib/input_uvc.so -d /dev/video0 -r 640x480 -f 28" -o "/usr/lib/output_http.so -p 8090 -w /var/www/mjpg_streamer"
This will send the stream over port 8090. Which can be accessed via URL through the following link (where alarmpi is the IP of the raspberry pi).
This works with browsers which can read mjpg streams. If you happen have a web-controlled servo and some tape, you can embed the stream in the website and have a rotatable webcam.